A high-pressure discharge lamp of the type in question is known, for example, from WO 2008/071543 A1. Said document describes a high-pressure discharge lamp having a single socket for a vehicle headlamp, the high-pressure discharge lamp having the following features:                a discharge vessel having two opposite sealed ends and a discharge chamber arranged between the sealed ends, a first sealed end extending into a lamp base and the second sealed end protruding out of the lamp base,        a first electrode which is fixed in the first sealed end of the discharge vessel and has an end on the discharge side extending into the discharge chamber,        a second electrode which is fixed in the second sealed end of the discharge vessel and has an end on the discharge side extending into the discharge chamber, and        a base flange arranged on the lamp base and defining a plane which is usable for adjusting the high-pressure discharge lamp in an optical system.        